Question: Liliana used $4$ dark power crystals to raise $14$ zombie soldiers. She wants to know how many zombie soldiers $(z)$ she can raise with $10$ dark power crystals. How many zombie soldiers can Liliana raise with $10$ power crystals?
We're dealing with a proportional relationship, so each ratio of power crystals to zombies must be equivalent. Here's one way to write the proportion: $\dfrac{z\text{ zombies}}{10\text{ crystals}} = \dfrac{14\text{ zombies}}{4\text{ crystals}}$ Now, solve the proportion for $z$ : $\begin{aligned} \dfrac{z}{10} &= \dfrac{14}{4} \\\\ \dfrac{z}{10} &= \dfrac{7}{2} \\\\ z &= \dfrac{7}{2} \cdot 10 \\\\ z &= \dfrac{7\cdot 10}{2} \\\\ z &= \dfrac{7\cdot \stackrel{5}{\cancel{10}} }{\underset{1}{\cancel2}} \\\\ z &= \dfrac{7 \cdot 5}{1} \\\\ z &= \dfrac{35}{1} \\\\ z &= 35 \end{aligned}$ Liliana can raise $35$ zombie soldiers with $10$ power crystals.